Abstract

A Boolean circuit of depth is a circuit comprised of AND, OR and NOT
gates arranged in at most layers. This class of circuits is one of
the few complexity classes where unconditional lower bounds, i.e.
computational impossibility results exist. Many of the bounds follow
from a deep connection between bounded-depth circuits and low-degree
multivariate polynomials.

In this talk we will discuss some of these connections. We will then
present a proof of the 1990 Linial-Nisan conjecture on the
computational power of bounded-depth circuits. The conjecture stated
that bounded-depth Boolean circuits of size cannot distinguish
inputs drawn from a -wise independent distributions from uniform
inputs, where .
The talk will be almost completely self-contained.